On the Shared Preferences of Two Bayesian Decision Makers

Seidenfeld, Teddy; Kadane, Joseph B.; Schervish, Mark J.

doi:10.2307/2027108

Cited by 98 publications

(57 citation statements)

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“…However, our aim is to call into question the assumption that group opinion should be represented by a single probability distribution when precision holds at the level of the individuals. In this effort, we extend a line of argument that uses limitative results concerning aggregation-results demonstrating the impossibility of jointly satisfying a set of formal pooling criteria for precise aggregation methods-as a springboard into IP (Walley, 1982;Seidenfeld et al, 1989). That is, the limitations of precise pooling motivate IP in the sense that certain IP models do satisfy desiderata for "group" opinion that precise models do not.…”

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confidence: 92%

Probabilistic Opinion Pooling with Imprecise Probabilities

Stewart

Quintana

2017

J Philos Logic

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Abstract. The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution (Madansky, 1964;Lehrer and Wagner, 1981;McConway, 1981;Bordley, 1982;Genest and Zidek, 1986;Mongin, 1995;Clemen and Winkler, 1999;Dietrich and List, 2014;Herzberg, 2014). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities (IP) by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi (1985), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus.

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confidence: 92%

Probabilistic Opinion Pooling with Imprecise Probabilities

Stewart

Quintana

2017

J Philos Logic

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“…At issue here is whether we should seek consensus in judgments of admissibility or in reasons for judgments of admissibility (probability, utility, etc.) (Seidenfeld et al, 1989). Conditional judgments of admissibility might be seen as a way of walking a line between these two views, but in any case, we can deliver the right results for either view by suitably constraining E.…”

Section: Conditional Choice With a Vacuous Second Tiermentioning

confidence: 99%

“…That account has it that a neutral position with respect to conflicting judgments of a particular type preserves the shared agreements between the parties and introduces no judgments over which there is disagreement (Levi, 1986;Seidenfeld et al, 1989). This way, no relevant questions are begged and further deliberation or inquiry can be undertaken from such a perspective.…”

Section: Conditional Choice With a Vacuous Second Tiermentioning

confidence: 99%

Conditional choice with a vacuous second tier

Stewart

2015

Synthese

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Abstract. This paper studies a generalization of rational choice theory. I briefly review the motivations that Helzner gives for his conditional choice construction (Helzner, 2013). Then, I focus on the important class of conditional choice functions with vacuous second tiers. This class is interesting for both formal and philosophical reasons. I argue that this class makes explicit one of conditional choice's normative motivations in terms of an account of neutrality advocated within a certain tradition in decision theory. The observations recorded-several of which are generalizations of central results in the standard theory of rational choice-are intended to provide further insight into how conditional choice generalizes the standard account and are offered as additional evidence of the fruitfulness of the conditional choice framework. Rational Choice and Decision Theory and Uncertainty and Value Conflict and Conditional Judgment Admissibility and PreferenceFor the received view of rationality, the concept of preference is central. This is true, too, for the expectation tradition in decision theory more generally, from early accounts of expected value to Savage's widely endorsed development of subjective expected utility theory (Savage, 1972(Savage, , originally published in 1954Helzner, MS). 1 According to the subjective expected utility tradition's account of decision making, a rational agent has a credal state that can be represented by a probability distribution over the relevant state space and values that can be represented by a cardinal utility function over the relevant space of outcomes. What rationality demands is that an agent's choices maximize expectation with respect to the indicated sort of probability and utility functions (Savage, 1972(Savage, , originally published in 1954Luce and Raiffa, 1957). Subjective expected utility induces a preference ordering on the set of alternatives and rational choices are those made in accordance with that ordering (or, provided an agent's preferences satisfy certain constraints, she can be represented as maximizing expected utility). Even many deviations from this view-from descriptive theories such as Kahneman and Tversky's prospect theory (1979) to normative accounts such as those of Ellsberg (1963) and Gärdenfors and Sahlin (1982)-retain the assumption of a preference ordering while surrendering other aspects of the expected utility tradition.But there is also a "persistent underground movement" that calls into question the normative status of the ordering assumption for preference (Seidenfeld, 1988). Thanks are due to John Collins, Jeff Helzner, Tobias Lessmeister, Isaac Levi, Yang Liu, Ignacio Ojea, Paul Pedersen, Hans Rott, and two anonymous referees for helpful comments and discussions.1 As Helzner points out, while Savage's work eximplifies the tradition of expected utility most familiar to economists, psychologists, and statisticians, perhaps the tradition descending from Richard Jeffrey (1983) is most well-known among philosophers.

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“…First, it may happen that existing beliefs are incomplete or vague [10,11,12], either because there is no resources to spend in their elicitation, or because experts are psychologically unable to specify precise probability values. Second, it may be the case that a group of experts disagrees on probability values, and no compromise can be reached other than the collection of their opinions [13,14]. Another reason to abandon a single probability measure is when one is interested in the robustness of inferences -that is, in evaluating how much inferences can change when probability values are allowed to vary [8,15,16].…”

Section: Risk Knightian Uncertainty and Sets Of Probabilitiesmentioning

confidence: 99%

Unifying Nondeterministic and Probabilistic Planning Through Imprecise Markov Decision Processes

Trevizan

Cozman

Barros

2006

Advances in Artificial Intelligence - IBERAMIA-SBIA 2006

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Abstract. This paper proposes an unifying formulation for nondeterministic and probabilistic planning. These two strands of AI planning have followed different strategies: while nondeterministic planning usually looks for minimax (or worst-case) policies, probabilistic planning attempts to maximize expected reward. In this paper we show that both problems are special cases of a more general approach, and we demonstrate that the resulting structures are Markov Decision Processes with Imprecise Probabilities (MDPIPs). We also show how existing algorithms for MDPIPs can be adapted to planning under uncertainty.

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On the Shared Preferences of Two Bayesian Decision Makers

Cited by 98 publications

References 0 publications

Probabilistic Opinion Pooling with Imprecise Probabilities

Probabilistic Opinion Pooling with Imprecise Probabilities

Conditional choice with a vacuous second tier

Unifying Nondeterministic and Probabilistic Planning Through Imprecise Markov Decision Processes

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